Thank you for visiting A circle has a radius of 10 inches Find the approximate length of the arc intersected by a central angle of tex frac 2 pi. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To find the length of the arc intersected by a central angle, you can use the following formula:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)} \][/tex]
Here's how you would solve it step-by-step:
1. Identify the radius of the circle: The problem states that the radius is 10 inches.
2. Identify the central angle: The central angle given is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
3. Calculate the arc length:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
This results in:
[tex]\[
\text{Arc Length} \approx 20.94 \text{ inches}
\][/tex]
So, the approximate length of the arc intersected by the central angle [tex]\(\frac{2\pi}{3}\)[/tex] is 20.94 inches.
Therefore, the correct answer from the options provided is 20.94 inches.
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)} \][/tex]
Here's how you would solve it step-by-step:
1. Identify the radius of the circle: The problem states that the radius is 10 inches.
2. Identify the central angle: The central angle given is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
3. Calculate the arc length:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
This results in:
[tex]\[
\text{Arc Length} \approx 20.94 \text{ inches}
\][/tex]
So, the approximate length of the arc intersected by the central angle [tex]\(\frac{2\pi}{3}\)[/tex] is 20.94 inches.
Therefore, the correct answer from the options provided is 20.94 inches.
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